US7333552B2 - Method for coding and decoding an information symbol - Google Patents

Method for coding and decoding an information symbol Download PDF

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US7333552B2
US7333552B2 US10/363,968 US36396803A US7333552B2 US 7333552 B2 US7333552 B2 US 7333552B2 US 36396803 A US36396803 A US 36396803A US 7333552 B2 US7333552 B2 US 7333552B2
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channel
symbol
sending
value
symbols
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US20040008797A1 (en
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Manfred Koslar
Rainer Hach
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Inpixon GmbH
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Nanotron Technologies GmbH
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03343—Arrangements at the transmitter end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03828—Arrangements for spectral shaping; Arrangements for providing signals with specified spectral properties
    • H04L25/03866—Arrangements for spectral shaping; Arrangements for providing signals with specified spectral properties using scrambling
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power

Definitions

  • the present invention pertains to a method for coding and decoding an information symbol or stream of information symbols to be transmitted across a transmission channel. Furthermore, the invention pertains to devices for encoding a signal to be transmitted and decoding a signal value received.
  • ISI inter-symbol interference
  • the perturbing influence of the transmission channel can be reduced by devices at the receiver side, such as equalizers or maximum likelihood sequence estimation.
  • precoding represents a way of reducing the perturbing influence of ISI caused by the transmission channel.
  • Tomlinson Method as described by M. Tomlinson in “New Automatic Equalizer Employing Modulo Arithmetic,” Electronics Letters, 25 Mar. 1971, Vol. 7, pp. 138-139, numerous investigations have been conducted on the topic of precoding and various precoding variants have been developed.
  • the invention provides a method and a device for the encoding and decoding of information signals by which the required computational expense can be diminished, especially at the receiving side.
  • a stable transmission of predistorted symbol streams across transmission channels with strong reflection can be achieved with little computational expense at the receiving side.
  • a channel symbol alphabet is defined, which is more powerful, i.e., it contains more elements, than the alphabet of the information symbols being transferred (information symbol alphabet). Due to the fact that the channel symbol alphabet is more powerful than the information symbol alphabet, the result is possibilities for choosing the form in which an information symbol can be transmitted by means of different channel symbols. Therefore, the encoding or precoding method proposed herein is designated hereafter as multiple-choice preceding (MCP). Said possibility of choice is utilized so that a transmission value is sent with the lowest possible energy at the sending side, while the ISI produced by it has minimal perturbation or is even constructive in effect.
  • MCP multiple-choice preceding
  • MCP Compared to known precoating methods, the advantage of MCP consists in the fact that no additional computational operations are required at the receiving side. This not only reduces the costs, but also any time delay or sources of error such as quantization errors or parameter inaccuracies. As a kind of side effect, in the case of constant symbol sequences MCP can take on the function of a scrambler (cf. Lochmann: Digitale germantechnik, Verlagtechnik GmbH, Berlin 1997, 2 nd edition, ISBN 3-241-01184-6) and thereby facilitates the bit sequence-independent symbol synchronization at the receiving side with high data rates.
  • a certain agreement with the present invention consists in that distances from constellation points (or constellation regions in the present invention) are determined and taken into account. In contrast to the present invention, however, all calculations take place at the receiving side and not, as in the present invention, at the sending side.
  • the teaching of DE 199 12 825 in no way achieves the goal of having the receiving side be organized as simple as possible.
  • the channel symbol alphabet differs from the information symbol alphabet also in the number of possible phase values of its elements. Because of the direct use of the complex plane, the problem of intensified signal dynamics at the receiving side does not occur in the present invention and an infinite predictable set of “sending values” is not required as in the Tomlinson-Harashima Method.
  • the position of an uncertainty region in the complex plane is defined by the channel properties and by the sending values which were sent in the past, and the size and shape of this uncertainty region are defined by the sending values to be sent in future.
  • the position of the uncertainty region is determined by an ISI component E ISIpost , which can be exactly calculated in advance by means of the channel properties and the sending values sent in the past.
  • An additional ISI component E ISIpre which is created by future sending values interacting with the channel properties, cannot be exactly computed in advance because of causality reasons.
  • the shape and size of the uncertainty region allow for the possible influence which E ISIpre might have in the detection of the signal currently being transmitted.
  • the choice at the sending side of the desired channel symbol which can be chosen at the receiving side is based on its position in relation to the presently calculated uncertainty region.
  • the channel properties can be determined preferably by means of the channel pulse response.
  • the channel pulse response can be found by measurement techniques, for example, and be updated in predetermined intervals of time.
  • This “minimal maximum value” is hereafter termed the “smallest correction value”.
  • the sending value “0” (physically nothing is sent) can occur if the presently calculated uncertainty region is situated in an area which leads with high probability to a decision at the receiving side for a channel symbol that can be selected for the transmission of the present information symbol. This means that the ISI produced by past sending values has constructive effect and is sufficient for transmitting the channel symbol selected for the present information symbol.
  • the distance used during the decoding one can preferably calculate a Euclidean distance or a Hamming distance. These quantities furnish a measure for the decision-making distance between different possible channel symbols.
  • the calculating arrangement provided in the encoding device can comprise a first memory arrangement for storing the sending values already sent, a second memory arrangement for storing of channel coefficients which describe the postoscillation of the transmission channel, a multiplication arrangement for multiplying the sending values already sent with the corresponding channel coefficients, and an addition arrangement for adding up the results of the multiplication.
  • the expected reception signal values can then be computed in advance in the calculating arrangement, preferably by means of the addition result, the selected channel symbol, and an expectation value taking into account the preoscillation behavior of the transmission channel. This makes it possible to factor in the preoscillation behavior of the transmission channel.
  • a prefilter adapted to the transmission channel can also be provided.
  • FIG. 1 a block diagram of a transmission system according to the preferred sample embodiment
  • FIG. 2 a block diagram of an encoder according to the preferred sample embodiment
  • FIG. 3 a flow chart of an encoding method according to the preferred sample embodiment
  • FIGS. 4A-4C sample representations of the smallest correction value and the computed sending value for a case decision as explained in the preferred sample embodiment
  • FIG. 5 a flow chart of a decoding method according to the preferred sample embodiment
  • FIG. 6 a representation to explain a decision distance used during the decoding
  • FIG. 7 a diagram to represent decision regions used in a BPSK encoding
  • FIG. 8 an example of a complex pulse response of a transmission channel
  • FIG. 9 a complex diagram to represent the constellation of a BPSK symbol stream present at the receiver input without using the encoding according to the invention
  • FIG. 10 a complex diagram to represent the constellation of a BPSK symbol stream present at the receiver input when using the encoding according to the invention
  • FIG. 11 a complex diagram to represent the constellation at the receiver input in the case of a constant sequence of identical information symbols making use of the encoding according to the invention
  • FIG. 12 a flow chart to show the calculation of a sending value in forward-looking MCP.
  • FIG. 1 shows a block diagram of the symbol flow in a baseband model during a transmission of information symbols making use of several selectable channel symbols (MCP method).
  • MCP method selectable channel symbols
  • the pre-encoder (f MCP ( ⁇ )) 10 selects a channel symbol which is desirable at the receiver input and from this calculates a sending value z i (tx) ⁇ Z (tx) to be sent out. This calculation makes use of both the channel properties and the sending values sent in the past.
  • z i ( tx ) f MCP ⁇ ( v i ( tx ) , h _ , z i - 1 ( tx ) , z i - 2 ( tx ) , ... ⁇ , z i - n ( tx ) ) , ( 1 )
  • the sending value z i (tx) generated in a pre-encoder 10 of a transmitter 100 by the MCP method is sent via the channel 20 .
  • the fundamental channel symbol y i (rx) is determined by means of a decider 31 .
  • a received information symbol v i (rx) is detected or determined by means of an assigner 32 , making use of a mapping function f( ⁇ ), which is a simple single-valued but not reversible mapping.
  • a detection error D err (z (rx) , y (rx) , v (tx) ) is defined according to the following equation (2), which can be computed in advance at the transmitter side.
  • D err ( ⁇ ) is dependent on the reception value z (rx) calculated in advance at the decider input, the channel symbol y (rx) detected from this, and the desired information symbol v (tx) which should appear at the receiver output:
  • BordDist (z, y) provides the decision-making distance (see FIG. 6 ). By this is meant the Euclidean distance between the value z and the limits of the certain decision-making region of the channel symbol y detected by the decider 31 .
  • the Hamming distance or another suitable quantity can also be used as the decision-making distance.
  • the detection error D err (z (rx) , y (rx) , v (tx) ) is a measure of the uncertainty with which an information symbol v (tx) is correctly detected for a given reception symbol z (rx) .
  • a negative detection error indicates that the reception symbol z (rx) lies within the certain decision-making region of a channel symbol y (rx) and that this channel symbol is mapped on the correct information symbol.
  • the receiver performs a detection in terms of symbols, that a reception value is sampled with a time delay of m symbol time steps relative to its sending time point, after which it is located at the amplitude maximum of the channel pulse response, and that the receiver 30 performs a phase synchronization so that the reception value sampled at the time point m is in correct phase.
  • the channel 20 has the time delay m and no preoscillation or postoscillation
  • ⁇ i,j is the Kronecker symbol.
  • the effective channel pulse response of the channel 20 located between the transmitter 100 and the receiver 30 has the following characteristic:
  • ⁇ 1, h m 1,
  • the first summand on the left side of equation (5) describes ISI components E ISIpost that can be described by sending values which were sent prior to the sending value z ⁇ m (tx) in time and are attributable to the postoscillation (post-cursor) of the channel, while the last summand describes the ISI components E ISIpre that are caused by preoscillation (pre-cursor) and are dependent on sending values that were sent after the sending value z ⁇ m (tx) in time and consequently were not yet known when the sending value z ⁇ m (tx) was sent.
  • This can be represented by the following equation (6):
  • the right side of the equation (6) shows that the reception value can be interpreted as the sum of a transmitted channel symbol and an error value caused by interferences.
  • a square region S (rx) (z) is defined by the following equation (9), within which the reception value is expected:
  • the size of the uncertainty region S (rx) depends on the preoscillation behavior (oscillation build-up behavior) of the channel 20 . If one further allows for the general requirement of sending out the lowest possible symbol energy in order to keep low any overmodulation distortions, the calculation of z ⁇ m (tx) leads to the following optimization problem:
  • the pre-encoder function provided in the pre-encoder 10 can be realized in the form of a table of values after the channel property is discovered.
  • the table of values can be realized, for example, as a table of values for probable types of channel pulse responses, and a selection can then be made using the measured channel property.
  • FIG. 2 shows a block diagram of the pre-encoder 10 according to the preferred sample embodiment, in which the indices indicated in equation (5) are used to identify the time sequence.
  • the information symbol v ⁇ m (tx) being transmitted is taken to an encoder 11 , which generates p channel symbols y 1 to yp selectable for v ⁇ m (tx) and supplies them to a symbol selector 12 .
  • the encoder 11 can be realized by a memory table or the like.
  • a symbol storage 14 is provided in the form of a parallel-readable shift register, in which the sending values z ⁇ m ⁇ 1 (tx) to z ⁇ n (tx) already sent are written in consecutively during each sending.
  • the number n-m of stored sending values thus corresponds to the postoscillation time of the channel 20 .
  • Another parallel-readable coefficient storage 13 serves to store the coefficients h m to h n of the channel 20 , and the coefficient h m is supplied to the symbol selector 12 in order to factor in the direct action of the channel 20 on the information symbol v ⁇ m (tx) being transmitted.
  • the channel coefficients h j are multiplied with the corresponding stored sending values z j in corresponding multiplication arrangements and added together in an addition arrangement, in order to obtain in this way a characteristic value for the particular postoscillation of the channel 20 , which is supplied to the symbol selector 12 and used to calculate the expected reception values or range of values (i.e., the uncertainty region S) used for the selection of the suitable channel symbol.
  • the channel symbol y selected by the symbol selector 12 and the uncertainty region S (rx) (E ISIpost ) calculated in the symbol selector are used by a sending value calculator 15 to calculate the present sending value z ⁇ m (tx) as described hereafter.
  • the blocks shown in FIG. 2 can also be realized, of course, as program routines for a signal processor or the like provided in the transmitter 100 .
  • FIG. 3 shows a flow chart of the encoding process according to the preferred sample embodiment.
  • step S 100 the pre- and postoscillation behavior of the channel 20 is first determined, for example, by means of a measured channel pulse response h of the channel 20 , and the corresponding coefficients are stored in memory.
  • the information symbol v i (tx) being transmitted and the past sending symbols z i ⁇ 1 (tx) ,z i ⁇ 2 (tx) , . . . ,z i ⁇ n+m (tx) stored in the symbol storage 14 are known, where n indicates the channel order and m the channel delay.
  • the sending value z i (tx) to be emitted at time i is determined as follows.
  • step S 101 the uncertainty region produced by the ISI for the reception at the receiver 30 at time i+m is calculated per equation (9a). This can be done, for example, by calculating the corner points of the uncertainty region S (rx) (E i+m ISIpost ).
  • l max arg l ⁇ ( max ⁇ (
  • j min arg j ⁇ ( min ⁇ (
  • ) ) ⁇ ⁇ j 1 , 2 , ... ⁇ ⁇ p , ( 12 ⁇ a )
  • the sending value z (diff) as determined per equation (12b) will be sent so as to enable a secure detection with low transmission energy and low associated ISI (S 103 ).
  • the uncertainty region S (rx) (E ISIpost ) is located inside the “inner region” and the smallest correction value z (diff) corresponds to the distance between the furthest corner point c 3 and the channel symbol y 1 selected on the basis of the least maximum corner distance. This smallest correction value z (diff) is then sent as the sending value to achieve the desired reception value.
  • the smallest correction value z (diff) corresponds to the distance between the furthest corner point c 2 and the channel symbol y 1 chosen on the basis of the least maximum corner distance.
  • a limiting of the region can then occur by limiting the complex components of the sent sending value according to the following equations (16a) and (16b), in order to limit the maximum transmission energy:
  • > r max ⁇ >real( z i (tx) ) sign(real( z i (tx) )) ⁇ r max (16a)
  • >r max ⁇ >imag( z i (tx) ) sign(imag( z i (tx) ) ⁇ r max (16b)
  • the region can also be limited by limiting the amplitude of the complex sent signal value to a maximum value.
  • step S 200 a reception value z is received and taken to the decider 31 .
  • the decider 31 compares the reception value with predetermined decision-making regions for the possible channel symbols y according to the channel symbols available Y, in order to determine the received symbol (S 201 ). This occurs according to equation (2).
  • the decision-making regions at the reception side can be the quadrants in the complex plane, for example.
  • FIG. 6 shows a general view of a decision-making region for a channel symbol y in the complex plane.
  • the decider 31 puts out the corresponding channel symbol y to the assigner 32 .
  • step S 202 of FIG. 5 a match-up between the discovered channel symbol y and the corresponding information symbol v takes place in the assigner 32 with the help of a mapping function f, which can be provided, for example, as a memory table or logic function in the assigner 32 .
  • the process then returns to step S 200 , waiting for the reception of a new signal value.
  • FIG. 7 shows the decision-making regions considered certain for the channel symbols. Calculation of the sending values is such that the reception values lie with high probability in the certain decision-making regions. Since a distinct decision always has to be made at the receiver side, it is permissible to allow expanded decision-making regions neighboring each other there, such as the complete quadrants.
  • FIG. 8 shows the complex channel pulse response of a low-preoscillation system in the symbol pulse.
  • a simple detector which detects the underlying information symbol v by means of the quadrant in which a reception symbol lies, would produce an error-free stream of reception symbols at the receiver output in this case.
  • the reception signal contains temporal changes which facilitate a synchronization at the receiver side, without requiring additional descrambling measures.
  • the method described in the present application can also be summarized by saying that one makes a selection from p possible representations (channel symbols) for an information symbol which is to be transmitted from a transmitter to a receiver and determines the sending value which is required for the selected channel symbol to appear in the receiver's input. Minimization of the energy of the sending value serves as the criterion of choice. Therefore, the invention can also be described as a symbolwise multiple-choice-precoding (MCP).
  • MCP symbolwise multiple-choice-precoding
  • One possibility of expanding the symbolwise MCP is a forward-looking MCP, as depicted in a flow chart per FIG. 12 .
  • L information symbols to be sent in future and p possible representations one gets a totality of p (L+1) representation sequences.
  • the flow chart contains an outer loop through p (L+1) representation sequences.
  • Each representation sequence consists of (L+1) channel symbols and the corresponding sending values.
  • an inner loop is represented in the flow chart.
  • the energy values of the sending values are added up.
  • the inner loop ends either when all (L+1) values have been computed or when the energy sum exceeds the previous minimum. In the latter case, a premature interruption is possible, since it is certain that the final overall energy of the particular representation sequence is greater than the final overall energy of at least one other previously computed representation sequence.
  • the representation sequence whose sum of sending energy values is minimal is known.
  • the selection criterion is the minimization of the overall energy of a sequence of sending values
  • the first channel symbol of the representation sequence with minimum sum of sending energy values is selected as the channel symbol for the current information symbol being sent.
  • the sending value is computed as a function of the selected channel symbol and sent out.
  • the special advantage of forward-looking MCP over symbolwise MCP consists in the minimization of the mean and maximum sending value energy.
  • the computation of the forward-looking MCP can be defined as a problem which consists in making a sequence of discrete decisions so that a cost function is minimized.
  • the described algorithm implicitly contains a scrambling function when the channels are sufficiently distortion-rich.
  • the desired channel symbol y (tx) can be randomly selected, for example. In this way, a good dynamics is ensured in the reception symbol sequence for each information symbol sequence and, thus, code transparency for the method.
  • the invented encoding method is based on the basic notion of a channel symbol alphabet which is more powerful than the information symbol alphabet, i.e., the channel symbol alphabet contains at least one more element than the information symbol alphabet.
  • the channel symbol alphabet contains at least one more element than the information symbol alphabet.
  • the MCP method can be used advantageously in applications, for example, where time-invariant channels with strong reflections are disrupting the communication between a base station and many subscriber stations as the main source of interference, such as WLL systems.
  • the MCP method can also be used advantageously in higher-stage PSK and in DPSK modulation methods or also in other suitable types of modulation.
  • bit sequence-independent synchronization is facilitated and thus can be made more cheap with MCP for all data rates.

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DE10044227A DE10044227A1 (de) 2000-09-07 2000-09-07 Verfahren zum Codieren und Decodieren eines Informationssymbols
PCT/EP2001/010140 WO2002021783A1 (de) 2000-09-07 2001-09-04 Verfahren zum codieren und decodieren eines informationssymbols

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WO2007014241A1 (en) * 2005-07-25 2007-02-01 Boston Scientific Scimed, Inc. Pelvic floor repair system
US8345727B2 (en) * 2008-05-13 2013-01-01 Metropolitan Area Networks, Inc. Communication system, apparatus, and methods
WO2010096948A1 (zh) * 2009-02-24 2010-09-02 上海贝尔股份有限公司 利用相位重新赋形实现的脏纸预编码方法和发射机
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US5159610A (en) 1989-05-12 1992-10-27 Codex Corporation Trellis precoding for modulation systems
EP0555013A2 (de) 1992-02-05 1993-08-11 AT&T Corp. Modulo-Dekoder
US5455839A (en) 1991-12-27 1995-10-03 Motorola, Inc. Device and method for precoding
DE4440947A1 (de) 1994-10-19 1996-04-25 Kommunikations Elektronik Verfahren zur digitalen Nachrichtenübertragung
US5570388A (en) 1994-09-27 1996-10-29 Digital Ocean, Inc. Method and apparatus using simple codes for the wireless transmission of non-data symbols
US5696769A (en) * 1994-11-08 1997-12-09 Lg Information & Communications, Ltd Decision error correcting method of a digital communication system and the digital communication system for the same
DE19912825C1 (de) 1999-03-22 2000-08-10 Siemens Ag Verfahren, Empfangseinrichtung und Funkstation zum Detektieren eines Datensymbols

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Publication number Priority date Publication date Assignee Title
US5159610A (en) 1989-05-12 1992-10-27 Codex Corporation Trellis precoding for modulation systems
US5455839A (en) 1991-12-27 1995-10-03 Motorola, Inc. Device and method for precoding
EP0555013A2 (de) 1992-02-05 1993-08-11 AT&T Corp. Modulo-Dekoder
US5570388A (en) 1994-09-27 1996-10-29 Digital Ocean, Inc. Method and apparatus using simple codes for the wireless transmission of non-data symbols
DE4440947A1 (de) 1994-10-19 1996-04-25 Kommunikations Elektronik Verfahren zur digitalen Nachrichtenübertragung
US5696769A (en) * 1994-11-08 1997-12-09 Lg Information & Communications, Ltd Decision error correcting method of a digital communication system and the digital communication system for the same
DE19912825C1 (de) 1999-03-22 2000-08-10 Siemens Ag Verfahren, Empfangseinrichtung und Funkstation zum Detektieren eines Datensymbols

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KR100549670B1 (ko) 2006-02-08
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WO2002021783A1 (de) 2002-03-14
ATE297624T1 (de) 2005-06-15
EP1317829B1 (de) 2005-06-08
DE50106469D1 (de) 2005-07-14
AU2001285923A1 (en) 2002-03-22
US20040008797A1 (en) 2004-01-15
EP1317829A1 (de) 2003-06-11
KR20030040447A (ko) 2003-05-22
DE10044227A1 (de) 2002-04-04

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